MathDB

L(n,k) is the lcm of k consecutive integers

Source: Canadian MO 2012

May 4, 2012

number theoryleast common multiplenumber theory proposed

Problem Statement

For any positive integers

n

and

k

, let

L(n,k)

be the least common multiple of the

k

consecutive integers

n,n+1,\ldots ,n+k-1

. Show that for any integer

b

, there exist integers

n

and

k

such that

L(n,k)>bL(n+1,k)